Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C67 ⋊ C2 |
| Sylow | C67 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | D268 |
| commutator, cosocle | C4×C67 | C23 |
| Frattini | C4 | C22×D67 |
| Fitting | C2×C8×C67 | C2 |
| socle | C2×C67 | C2×D4 |
| hypercenter | C2×C8 | D67 |
| hypocenter | C67 | #135 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ C2×C8 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1072 |
Polycyclic presentation:
2^5,67|c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^66,d^b=de,f^b=f^66542 conjugacy classes — view the full character table.
| maximal subgroup of | #16863202, #16863204, #16863205, … |
| maximal normal subgroup of | #16863202, #16863204, #16863205, … |
| maximal quotient of | #16863393, #16863434, C4×D536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 168);